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Question

(b) Consider the MAP estimate,

θ^MAP=argmax⁡θp(θ∣D).(3.47)\hat{\theta}_{MAP} = \operatorname*{argmax}_\theta p(\theta|\mathcal{D}). \quad (3.47)

How does it differ from the least squares estimate and the weighted-least squares estimate? What is the role of the terms that were not present before? Is there any advantage in setting them to anything other than zero?